C H A P T E R 2 Polynomial and Rational Functions

111.
113.
115.
117.
12x 2 11x 5 0 112.
3x 14x 5 0
3x 1 0 ⇒ x 1
3
4x 5 0 ⇒ x 5
4
x 2 2x 21 0 114.
x 2 2x 1 2 21 1 0
x 1 2 22 0
x 1 2 22
x 1 ±22
x 1 ± 22
2 x 2 5x 20 0 116.
2 x2 5 x 20 0
2
5 2 x 4 2
185
2
0
8 x2 5
2 x 5
4 2 25
20 0
8
fx x 4 2
Common function:
5
x 4 2
185
16
y x 2
Transformation: Horizontal
shift four units to the left
x 5
±185
4 4
x
5 ± 185
4
−7 −6 −5 −4 −3 −2 −1 −1
7
6
5
4
3
2
1
y
1
x
Section 2.2 Polynomial Functions of Higher Degree 167
118.
x 2 24x 144 0
x 12 2 0
x 12 0
x 2 8x 2 0
x 4 2 14
x 12
x 2 8x 2
x 2 8x 16 2 16
x 4 ±14
3x 2 4x 9 0
x2 4
x 3 0
3
x2 4
x 3
3
x 4 ± 14
x2 4 4 4
x 3
3 9 9
2
x 3 2
31
9
x 2 31
± 3 9
x 2 31
±
3 3
x
f x 3 x 2
2 ± 31
3
Reflection in the x-axis
and vertical shift of three
units upward of y x 2
119. fx x 1 5 y
120. f x 7 x 6
Common function: y x
1
Horizontal shift of six units
Transformation: Horizontal
shift one unit to the left and
a vertical shift five units
downward
−3 −2 −1
−1
−2
−3
1 2 3
x
to the right, reflection in the
x-axis, and vertical shift of
seven units upward
of y x
−5
4
2
1
−4 −3 −1
−1
15
12
9
6
3
y
−2
−3
−4
y
1 3 4
−3 3 6 9 12 15
−3
x
x